Built for speed: strain in the cartilaginous vertebral columns of sharks

In most bony fishes vertebral column strain during locomotion is almost exclusively in the intervertebral joints, and when these joints move there is the potential to store and release strain energy. Since cartilaginous fishes have poorly mineralized vertebral centra, we tested whether the vertebral bodies undergo substantial strain and thus may be sites of energy storage during locomotion. We measured axial strains of the intervertebral joints and vertebrae in vivo and ex vivo to characterize the dynamic behavior of the vertebral column. We used sonomicrometry to directly measure in vivo and in situ strains of intervertebral joints and vertebrae of Squalus acanthias swimming in a flume. For ex vivo measurements, we used a materials testing system to dynamically bend segments of vertebral column at frequencies ranging from 0.25 to 1.00 Hz and a range of physiologically relevant curvatures, which were determined using a kinematic analysis. The vertebral centra of S. acanthias undergo strain during in vivo volitional movements as well as in situ passive movements. Moreover, when isolated segments of vertebral column were tested during mechanical bending, we measured the same magnitudes of strain. These data support our hypothesis that vertebral column strain in lateral bending is not limited to the intervertebral joints. In histological sections, we found that the vertebral column of S. acanthias has an intracentral canal that is open and covered with a velum layer. An open intracentral canal may indicate that the centra are acting as tunics around some sections of a hydrostat, effectively stiffening the vertebral column. These data suggest that the entire vertebral column of sharks, both joints and centra, is mechanically engaged as a dynamic spring during locomotion.     

Red and white muscle activity and kinematics of the escape response of the bluegill sunfish during swimming

Summary We quantified midline kinematics with synchronized electromyograms (emgs) from the red and white muscles on both sides of bluegill sunfish (Lepomis macrochirus) during escape behaviors which were elicited from fish both at a standstill and during steady speed swimming. Analyses of variance determined whether or not kinematic and emg variables differed significantly between muscle fiber types, among longitudinal positions, and between swimming versus standstill trials.At a given longitudinal location, both the red and white muscle were usually activated synchronously during both stages of the escape behavior. Stage 1 emg onsets were synchronous; however, the mean durations of stage 1 emgs showed a significant increase posteriorly from about 11 to 15 ms. Stage 2 emgs had significant posterior propagation, but the duration of the stage 2 emgs was constant (17 ms). Posterior emgs from both stages occurred during lengthening of the contractile tissue (as indicated by lateral bending). Steady swimming activity was confined to red muscle bursts which were propagated posteriorly and had significant posterior decrease in duration from about 50% to 37% of a cycle. Fish performed escape responses during all phases of the steady swimming motor pattern. All kinematic events were propagated posteriorly. Furthermore, no distinct kinematic event corresponded to the time intervals of the stage 1 and 2 emgs. The rate of propagation of kinematic events was always slower than that of the muscle activity. The phase relationship between lateral displacement and lateral bending also changed along the length of the fish. Escape responses performed during swimming averaged smaller amplitudes of stage 2 posterior lateral displacement; however, most other kinematic and emg variables did not vary significantly between these two treatments.Abbreviations A angle of lateral flexion (bending) of midline at a single point in time - A1, A2 change in A from T₀ to T₁ and from T₁ to T₂ - AMX maximal lateral flexion concave towards the side of the stage 1 emg - AMXR equals AMX minus A at T₀ - AT1, AT2 lateral flexion at T₁ and T₂ - DUR1, DUR2 durations of stage 1 and stage 2 emgs - emg electromyogram - ON2 onset time of stage 2 emg - RELDUR relative duration of steady swimming emg - T₀, T₁, T₂ times of stage 1 emg onset, latest stage 1 emg offset and latest stage 2 emg offset standardized such that T₀ = 0 - TAMX, TAMN, TYMX times of maximal lateral flexion, no lateral flexion and maximum lateral displacement - Y1, Y2 amounts of lateral displacement from T₀ to T₁ and from T₁ to T₂ - YMXR relative amount of lateral displacement from T₀ to TYMX     

The elongation of the human cervical vertebral column

Cervical vertebral elongation has been studied using serial cephalometric radiographs of 32 children examined regularly from 0.25 to 17 years. Mean vertebral body heights increased rapidly to about 2.5 years and then decelerated except for a spurt at about the age of peak height velocity. There were only small sex differences in vertebral body elongation to 12 years. From then to 15 years, the vertebral body heights in the girls exceeded those in the boys; later this sex difference was reversed. There was no pubertal spurt in disc elongation. The correlation coefficients were negative between vertebral body heights and the heights of adjoining intervertebral discs, e.g., body C3 and disc C3–4, but those between body heights or between disc heights were positive. The heights of adjacent cervical vertebral bodies were correlated more highly than the heights of non-adjacent bodies. There was a similar pattern of differences between correlation coefficients for the heights of adjacent and non-adjacent intervertebral discs.     

Variability of vertebral column measurements in Lithuanian paleopopulation

An analysis of measurements (anterior and posterior heights and middle body breadth) of 6,357 vertebrae and 336 sacral bones (length, superior breadth and promontory angle) of 539 adult persons from the 1st and the 2nd millennium burial grounds was performed. It was established that longitudinal and transversal measurements are rather weakly correlated. The factor of sex plays a major role in variability of vertebral measurements (up t0 40% from the total sum of factors). Certain sexual differences in a vertebral body form were also noted. The age has slight though significant influence (up to 8%) on vertebral body breadths, that was probably connected with age-related degenerative changes. The influence of the secular factor on vertebral variability was minimal. Only slight to moderate correlations with total body measurements were found. The conclusion was made that vertebral column measurements are of little value in interpopulational comparisons, at least for Europid samples, butthey could be of considerable interest for forensic anthropology.     

Osteological development of the vertebral column and of the caudal complex in Dentex dentex

Osteological development of the vertebral column and caudal complex in common dentex was described under extensive larval rearing conditions. Generally, the cartilaginous bones developed prior to the membranous bones. The development of the axial skeleton began with the formation of the hypural 1, the neural arches 2 and 3, as well as the haemal arches 1–8 at 4·8, 4·9 and 5·0 mm total length ( L _T, measured in vivo ), respectively. By 7·5 mm L _T, all the cartilaginous elements were formed, except for the ventral ribs, which formed between the range of 8·4–18·0 mm L _T. The caudal lepidotrichia were the first membranous bones to appear (5·3 mm L _T) and attain their full meristic count (7·4 mm L _T), followed by the vertebral centra, which formed between 6·6 and 9·7 mm L _T. By 25·0 mm L _T, all the elements were fully ossified except for the ventral ribs. The developmental direction and order of all the elements were studied with respect to their formation and ossification. The results were discussed in the contexts of ichthyoplankton, ecology and aquaculture. Compared with other Sparidae species, common dentex followed a pattern of relatively rapid rate of osteological development.     

Computational and mathematical modeling of the effects of tailbeat frequency and flexural stiffness in swimming fish

In this paper we describe how we combine computational and mathematical models to form virtual fish to explore different hypotheses about the impact of centra. We show how we create simulation models using a combination of a mathematical model of a fish-like robot using caudal fin propulsion, a propulsion model, and an optimizer, to explore the impact of centra under various scenarios. The optimizer uses the mathematical model to construct valid configurations of the digital robot and uses the utility function and propulsion model to evaluate the performance of each configuration. The evaluations are used to explore the adaptive landscape and find high-performing configurations. Our results show that the high-performing configurations have both increased (flexural) stiffness of the tail and higher tailbeat frequencies.     

Prezygapophyseal articular facet shape in the catarrhine thoracolumbar vertebral column

Two contrasting patterns of lumbar vertebral morphology generally characterize anthropoids. “Long‐backed” monkeys are distinguished from “short‐backed” apes [Benton: The baboon in medical research, Vol. 2 (1967:201)] with respect to several vertebral features thought to afford greater spinal flexibility in the former and spinal rigidity in the latter. Yet, discussions of spinal mobility are lacking important functional insight that can be gained by analysis of the zygapophyses, the spine's synovial joints responsible for allowing and resisting intervertebral movements. Here, prezygapophyseal articular facet (PAF) shape in the thoracolumbar spine of Papio, Hylobates, Pongo, Gorilla, and Pan is evaluated in the context of the “long‐backed” versus “short‐backed” model. A three‐dimensional geometric morphometric approach is used to examine how PAF shape changes along the thoracolumbar vertebral column of each taxon and how PAF shape varies across taxa at corresponding vertebral levels. The thoracolumbar transition in PAF shape differs between Papio and the hominoids, between Hylobates and the great apes, and to a lesser extent, among great apes. At the level of the first lumbar vertebra, the PAF shape of Papio is distinguished from that of hominoids. At the level of the second lumbar vertebra, there is variation to some extent among all taxa. These findings suggest that morphological and functional distinctions in primate vertebral anatomy may be more complex than suggested by a “long‐backed” versus “short‐backed” dichotomy. Am J Phys Anthropol 142:600–612, 2010. © 2010 Wiley‐Liss, Inc.     

Substrate stiffness regulates apoptosis and the mRNA expression of extracellular matrix regulatory genes in the rat annular cells

Cells are subjected to static tension of different magnitudes when cultured on substrates with different stiffnesses. It has long been recognized that mechanical stress is an important modulator of the intervertebral disc degeneration. Here we studied the influence of substrate stiffness on cell morphology, apoptosis and extracellular matrix (ECM) metabolism of the rat annulus fibrosus (AF) cells which are known to be mechanosensitive cells. Polyacrylamide gel substrates with three different stiffnesses were prepared by varying the concentration of acrylamide and bisacrylamide, and the elastic modulus of the different gel substrates were measured with atomic force microscopy (AFM). First-passage rat annular cells were cultured on soft, intermediate, rigid substrates or plastics for 24 or 48 h. The percentages of apoptotic cells were detected by flow cytometry and caspase-3 activity, and morphologic changes were visualized by Hoechst 33258 staining and F-actin staining. In addition, the expression of ECM genes (Col1α1, Col2α1, aggrecan, MMP-3, MMP-13 and ADAMTS-5) were analyzed by RT-PCR. The three different substrates had elastic moduli varying between 1 ± 0.23 kPa (soft, 5% gel with 0.06% bis), 32 ± 2.89 kPa (intermediate, 10% gel with 0.13% bis) and 63 ± 3.45 kPa (rigid, 10% gel with 0.26% bis) with a thickness about 60-70 μm. Most of the rat AF cells appeared small and rounded, and lost most of their stress fibers when cultured on soft substrate. There was a significant increase in the percentage of apoptotic cells in the rat AF cells cultured on soft and intermediate substrates relative to those on plastic surface, with a parallel decrease in the area of cell spreading and nucleus. The AF cells grown on intermediate or rigid substrate had reduced expression of Col1α1, Col2α1 and aggrecan and enhanced expression of MMP-3, MMP-13, and ADAMTS-5 at 24 h or 48 h, respectively, relative to those cultured on plastic surface. Conversely, we observed an up-regulation of Col2α1 and aggrecan and no change in the gene expression of MMP-3, MMP-13, and ADAMTS-5 in AF cells on soft substrates. Rat AF cells are sensitive to substrate stiffness which can regulate the morphology, growth, apoptosis and ECM metabolism of rat AF cells, thus indicating the importance of substrate choice for cell transplantation and regeneration for the treatment of disc degeneration using tissue-engineering technique.     

Composition of the excitatory drive during swimming in two amphibian embryos: Rana and Bufo

It has recently been shown that spinal neurons in Xenopus embryos receive cholinergic and electrotonic excitation during swimming, in addition to the well documented excitatory amino acid (EAA)-mediated excitation. We have now examined the composition of the excitatory drive during swimming in embryos of two further amphibian species, Rana and Bufo, which have somewhat different motor patterns. Localised applications of antagonists show that presumed motoneurons in Rana and Bufo embryos receive both cholinergic and EAA input during swimming. There is also a further chemical component which is blocked by Cd²⁺ and a small Cd²⁺-insensitive component, which is usually non-rhythmic. Rhythmic Cd²⁺-insensitive components, presumed to be phasic electrotonic potentials, were only seen in a small proportion of Bufo neurons and in no Rana neurons. While EAA and cholinergic inputs therefore appear to be consistent features of excitatory drive for swimming in amphibian embryo motoneurons, electrotonic input apparently occurs less commonly. Antagonist specificity was tested using applied agonists in Rana. Results of these tests also suggested that the further, unidentified Cd²⁺-sensitive component seen during swimming could represent an incomplete block of AMPA receptor-mediated excitation.Abbreviations AMPA -Amino-3-hydroxy-5-methyl- 4-isoxazolepropionic acid - CNQX 6-Cyano-7- nitroquinoxaline-2,3-dione - D-AP5 D(-)-2- Amino-5-phosphonopentanoic acid - DHE Dihydro--erythroidin - DMPP 1,1-dimethyl-4- phenylpiperazinium - HEPES N-[2-hydroxyethyl] piperazine-N-[2-ethanesulphonic acid] - NMDA N-methyl-D-aspartic acid     

Regional variation in morphology of vertebral centra and intervertebral joints in striped bass,Morone saxatilis

The vertebral column of fishes has traditionally been divided into just two distinct regions, abdominal and caudal. Recently, however, developmental, morphological, and mechanical investigations have brought this traditional regionalization scheme into question. Alternative regionalization schema advocate the division of the abdominal vertebrae into cervical, abdominal, and in some cases, transitional regions. Here, we investigate regional variation at the level of the vertebrae and intervertebral joint (IVJ) tissues in the striped bass, Morone saxatilis. We use gross dissection, histology, and polarized light imaging to quantify vertebral height, width, length, IVJ length, IVJ tissue volume and cross‐sectional area, and vertical septum fiber populations, and angles of insertion. Our results reveal regional differences between the first four (most rostral) abdominal vertebrae and IVJs and the next six abdominal vertebrae and IVJs, supporting the recognition of a distinct cervical region. We found significant variation in vertebral length, width, and height from cranial to caudal. In addition, we see a significant decline in the volume of notochordal cells and the cross‐sectional area of the fibrous sheath from cranial to caudal. Further, polarized light imaging revealed four distinct fiber populations within the vertical septum in the cervical and abdominal regions in contrast with just one fiber population found in the caudal region. Measurement of the insertion angles of these fiber populations revealed significant differences between the cervical and abdominal regions. Differences in vertebral, IVJ, and vertical septum morphology all predict greater range of motion and decreased stiffness in the caudal region of the fish compared with the cervical and abdominal regions. J. Morphol., 2012. © 2011 Wiley Periodicals, Inc.     

Prey capture by Luciocephalus pulcher: implications for models of jaw protrusion in teleost fishes

Synopsis Luciocephalus pulcher possesses one of the most protrusible jaws known among teleosts, the premaxillae extending anteriorly a distance of 33% of the head length during feeding. Jaw bone movement during feeding proceeds according to a stereotypical pattern and resembles that of other teleosts except for extreme cranial elevation and premaxillary protrusion. Anatomical specializations associated with cranial elevation include: a highly modified first vertebra with a separate neural spine, articular fossae on the posterior aspect, greatly enlarged zygapophyses on the second vertebra with complex articular condyles, and highly pinnate multi-layered epaxial musculature with multiple tendinous insertions on the skull. Luciocephalus, despite the extreme jaw protrusion, does not use suction during prey capture: rather, the prey is captured by a rapid lunge (peak velocity of about 150 cm per sec) and is surrounded by the open mouth. Previous hypotheses of the function of upper jaw protrusion are reviewed in relation to jaw movements inLuciocephalus. Protrusion is not obligatorily linked with suction feeding; behavioral aspects of the feeding process limit the possible range of biological roles of a given morphological specialization, and make prediction of role from structure risky.     

The skull and vertebral column pathology of Ancient Egyptians. A study of the Marro Collection

The skull and vertebral column pathology of the Ancient Egyptian skeletal remains of the Marro Collection (1118 individuals) is mainly represented by “common” degenerative and inflammatory osteo-articular alterations. Apart from these, three cases of ankylosing spondylitis and two cases of probable multiple myeloma are described in detail. The frequency of these conditions seems to be almost the same as in modern times. Furthermore, a skull with larger osteolitic areas of probable metastatic origin is described.     

Morphology,mechanics, and locomotion: the relation between the notochord and swimming motions in sturgeon

Synopsis To examine the relation between morphology and performance, notochordal morphology was correlated with notochordal mechanics and with steady swimming motions in white sturgeon, Acipenser transmontanus. In a still-water tank, motions of four sturgeon varied with changes in swimming speed and axial position along the body. For a 1..34 m sturgeon, slow and fast swimming modes were distinguished, with speeds at the fast mode more than two times those at the slow mode without changes in tailbeat frequency. This increase in speed is correlated with an increase in the body's maximal midline curvature (m^–1), suggesting a role for curvature-related mechanical properties of the notochord. Maximal midline curvature also varied with axial position, and surprisingly was uncorrelated with axial changes in the notochord's cross-sectional shape - as measured by height, width, inner diameter, and lateral thickness of the sheaths. On the other hand, maximal midline curvature was negatively correlated with the axial changes in the notochord's angular stiffness (N m rad^–1) and change in internal pressure (% change from baseline of 58.6 kPa), both of which were measured during in vitro bending tests. In vivo curvature and in vitro angular stiffness were then used to estimate the bending moments (Nm) in the notochord during swimming. In the precaudal notochord, the axial pattern of maximal stiffness moments was congruent with the pattern of maximal notochordal curvature in the precaudal region, but in the caudal notochord maximal angular stiffness was located craniad to maximal curvature. One interpretation of this pattern is that the precaudal notochord resists bending moments generated by the muscles and that the caudal notochord resists bending moments generated by hydrodynamic forces acting on the tail.     

Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis: II. Fast running

We have combined kinematic and electromyogram (EMG) analysis of running Blaberus discoidalis to examine how middle and hind leg kinematics vary with running speed and how the fast depressor coxa (Df) and fast extensor tibia (FETi) motor neurons affect kinematic parameters. In the range 2.5–10 Hz, B. discoidalis increases step frequency by altering the joint velocity and by reducing the time required for the transition from flexion to extension. For both Df and FETi the timing of recruitment coincides with the maximal frequency seen for the respective slow motor neurons. Df is first recruited at the beginning of coxa-femur (CF) extension. FETi is recruited in the latter half of femur-tibia (FT) extension during stance. Single muscle potentials produced by these fast motor neurons do not have pronounced effects on joint angular velocity during running. The transition from CF flexion to extension was abbreviated in those cycles with a Df potential occurring during the transition. One effect of Df activity during running may be to phase shift the beginning of joint extension so that the transition is sharpened. FETi is associated with greater FT extension at higher running speeds and may be necessary to overcome high joint torques at extended FT joint angles. Accepted: 24 May 1997     

Dynamic changes in body form during swimming in the water snake Nerodia sipedon

Video records of swimming water snakes show that during moderate to rapid swimming, the rear half to two-thirds of the trunk is compressed laterally, approaching the body form of some sea snakes. Body form of swimming snakes differed significantly from their shape when resting on a flat surface or when anesthetized and suspended in water. The extent of lateral flattening is positively correlated with swimming speed, a relationship generally supported by tests of trunk models in a flow tank. In Nerodia, the ability to temporarily flatten the trunk depends on kinetic costovertebral joints, a large compressible body cavity, and the absence of ventral skeletal support - features found in most snakes. Histological studies and manipulations of partially dissected preserved specimens showed that the resting angle of the ribs is maintained by localized elastic hypertrophy of the costovertebral capsular ligament. Trunk form during swimming in Nerodia is proposed to arise from anteromedial movement of the distal rib powered by deep muscles acting in concert with those proposed to generate undulation of the vertebral column.     

Variability and constraint in the mammalian vertebral column

Patterns of vertebral variation across mammals have seldom been quantified, making it difficult to test hypotheses of covariation within the axial skeleton and mechanisms behind the high level of vertebral conservatism among mammals. We examined variation in vertebral counts within 42 species of mammals, representing monotremes, marsupials and major clades of placentals. These data show that xenarthrans and afrotherians have, on average, a high proportion of individuals with meristic deviations from species' median series counts. Monotremes, xenarthrans, afrotherians and primates show relatively high variation in thoracolumbar vertebral count. Among the clades sampled in our dataset, rodents are the least variable, with several species not showing any deviations from median vertebral counts, or vertebral anomalies such as asymmetric ribs or transitional vertebrae. Most mammals show significant correlations between sacral position and length of the rib cage; only a few show a correlation between sacral position and number of sternebrae. The former result is consistent with the hypothesis that adult axial skeletal structures patterned by distinct mesodermal tissues are modular and covary; the latter is not. Variable levels of correlation among these structures may indicate that the boundaries of prim/abaxial mesodermal precursors of the axial skeleton are not uniform across species. We do not find evidence for a higher frequency of vertebral anomalies in our sample of embryos or neonates than in post-natal individuals of any species, contrary to the hypothesis that stabilizing selection plays a major role in vertebral patterning.     

Development of the vertebral column and caudal complex in a flyingfish,Parexocoetus mento mento (Teleostei: Exocoetidae)

The developmental pattern of the vertebral column and caudal complex in juvenile (16.9 mm SL) to adult (112.2 mm SL)Parexocoetus mento mento is described Juvenile external caudal morphology was similar to the adult condition, although juveniles exhibited various internal ontogenetic changes. Osteological develoment was almost completed at 60–69 mm SL. Complete ossification of the vertebral column and caudal complex appeared to be the optimal condition giving strength for flight. Loss of perforations in the centra, neural and haemal arches may be consistent with the rigid and straightened body position during take-off. Some ontogenetic changes in the caudal complex were related to functional aspects. Ankylosis of the NPU2 spur to the uroneural notch, fusion of hypurals 3+4 and 5 and the elongated hypural 1+2 (lower hypural) were linked to the acquisition of stability and strength in the caudal complex.     

Evidence for a role of antagonistic cocontraction in controlling trunk stiffness during lifting

Activity of the abdominal muscles during symmetric lifting has been a consistent finding in many studies. It has been hypothesized that this antagonistic coactivation increases trunk stiffness to provide stability to the spine. To test this, we investigated whether abdominal activity in lifting is increased in response to destabilizing conditions.

Ten healthy male subjects lifted 35 l containers containing 15 l of water (unstable condition), or ice (stable condition). 3D-kinematics, ground reaction forces, and EMG of selected trunk muscles were recorded. Euler angles of the thorax relative to the pelvis were determined. Inverse dynamics was used to calculate moments about L5S1. Averaged normalized abdominal EMG activity was calculated to express coactivation and an EMG-driven trunk muscle model was used to estimate the flexor moment produced by these muscles and to estimate the L5S1 compression force.

Abdominal coactivation was significantly higher when lifting the unstable load. This coincided with significant increases in estimated moments produced by the antagonist muscles and in estimated compression forces on the L5S1 disc, except at the instant of the peak moment about L5S1. The lifting style was not affected by load instability as evidenced by the absence of effects on moments about L5S1 and angles of the thorax relative to the pelvis. The data support the interpretation of abdominal cocontraction during lifting as subserving spinal stability. An alternative function of the increased trunk stiffness due to cocontraction might be to achieve more precise control over the trajectory of lifted weight in order to avoid sloshing of the water mass in the box and the consequent perturbations.     

Empirical analysis of the influence of swimming pattern on the net energetic cost of swimming in fishes

We tested the hypothesis that the energetics of swimming in a flume accurately represent the costs of various spontaneous movements using empirical relationships between fish swimming costs, weight, and speed for three swimming patterns: (1) 'forced swimming' corresponded to movements adopted by fish forced to swim against a unidirectional current of constant velocity; (2) 'directed swimming' was defined as quasi-rectilinear movements executed at relatively constant speeds in a stationary body of water and (3) 'routine swimming' was characterized by marked changes in swimming direction and speed. Weight and speed explained between 76% (routine swimming) and 80% (forced swimming) of net swimming cost variability. Net costs associated with different swimming patterns were compared using ratios of model predictions (swimming cost ratio; SCR) for various weight and speed combinations. Routine swimming was the most expensive swimming pattern (SCR for routine and forced swimming =6.4 to 14.0) followed by directed (SCR for directed and forced swimming =0.9 to 2.8), and forced swimming. The magnitude of the difference between the net costs of forced and spontaneous swimming increases with movement complexity and decreases as fish weight increases.     

Pendular mechanics and the kinematics and energetics of brachiating locomotion

Because brachiating locomotion is characterized by a pattern of swinging movements, brachiation has often been analogized to pendular motion, and aspects of the mechanics of pendular systems have been used to provide insight into both energetic and structural design aspects of this locomotor mode. However, there are several limitations to this approach. First, the motions of brachiating animals only approximate pendular motion, and therefore the energetics of these two systems are only roughly comparable. Second, the kinematic similarity between brachiation and pendular motion will be maximal at only one velocity, and the correspondence will be even less at greater or lesser speeds. Third, all forms of terrestrial locomotion that involve the use of limbs incorporate elements of pendular systems, and therefore brachiation is not unusual in this respect. Finally, it has been suggested that the mechanics of pendular motion will constrain the maximum attainable body size of brachiating animals and that this mechanical situation explains the lack of brachiating primates of greater than 30-kg body size; the present analysis provides evidence that the constraints on body size are far less strict than previously indicated and that extrinsic factors such as the geometry of the forest environment are more likely to dictate maximum body size for brachiators.